Graph-structured data is prevalent in the real world. Recently, due to the powerful emergent capabilities, Large Language Models (LLMs) have shown promising performance in modeling graphs. The key to effectively applying LLMs on graphs is converting graph data into a format LLMs can comprehend. Graph-to-token approaches are popular in enabling LLMs to process graph information. They transform graphs into sequences of tokens and align them with text tokens through instruction tuning, where self-supervised instruction tuning helps LLMs acquire general knowledge about graphs, and supervised fine-tuning specializes LLMs for the downstream tasks on graphs. Despite their initial success, we find that existing methods have a misalignment between self-supervised tasks and supervised downstream tasks, resulting in negative transfer from self-supervised fine-tuning to downstream tasks. To address these issues, we propose Graph Alignment Large Language Models (GALLM) to benefit from aligned task templates. In the self-supervised tuning stage, we introduce a novel text matching task using templates aligned with downstream tasks. In the task-specific tuning stage, we propose two category prompt methods that learn supervision information from additional explanation with further aligned templates. Experimental evaluations on four datasets demonstrate substantial improvements in supervised learning, multi-dataset generalizability, and particularly in zero-shot capability, highlighting the model's potential as a graph foundation model.